Ties between Hungary and the United Kingdom rest on "solid foundations" and are characterized by "mutual respect" and "common interests and goals", Orbán wrote.
Hungary's government is committed to further strengthening cooperation with the United Kingdom and remains a loyal ally, he added.
Minister of Foreign Affairs and Trade Péter Szijjártó congratulated Liz Truss on Monday, saying "As a colleague, we worked very well together, she has always been a very fair negotiating partner."